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On Combined Connectives

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Abstract

Combined connectives arise in combined logics. In fibrings, such combined connectives are known as shared connectives and inherit the logical properties of each component. A new way of combining connectives (and other language constructors of propositional nature) is proposed by inheriting only the common logical properties of the components. A sound and complete calculus is provided for reasoning about the latter. The calculus is shown to be a conservative extension of the original calculus. Examples are provided contributing to a better understanding of what are the common properties of any two constructors, say disjunction and conjunction.

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Authors and Affiliations

  1. Dep. Mathematics, Instituto Superior Técnico, Universidade Técnica de Lisboa, SQIG, Instituto de Telecomunicações, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    A. Sernadas, C. Sernadas & J. Rasga

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  1. A. Sernadas
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  2. C. Sernadas
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  3. J. Rasga
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Correspondence to A. Sernadas.

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Sernadas, A., Sernadas, C. & Rasga, J. On Combined Connectives. Log. Univers. 5, 205–224 (2011). https://doi.org/10.1007/s11787-011-0032-7

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  • DOI: https://doi.org/10.1007/s11787-011-0032-7

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